TABULACIÓN E INTERPRETACION DE DATOS

Before proceeding to a presentation and discussion of the empirical results, our estimates of the Fama-MacBeth regression coefficients are adjusted for autocorrelation using a method first used by Pontiff (1996) and subsequently used by Cornett et al. (2008), Irvine and Pontiff (2009), amongst others. The adjusted versions of the coefficient estimates and their standard errors are obtained by regressing the time-series of the parameter estimates on an intercept term and modeling the residuals as a sixth-order autoregressive process. The standard error of the intercept is then the corrected standard error for that coefficient. As long as the sixth- order autoregressive process captures all of the serial dependence, these standard errors are not biased by serial or cross-sectional correlation.

Furthermore, in this and subsequent sections of the essay, we not only examine statistical significance but also the elasticities of some of the variables that have statistical significance using two measures. The first measure is obtained by multiplying the estimated coefficient of an independent variable by the ratio of that variable’s mean to the mean of the dependent variable. The second measure is obtained by first multiplying the estimated coefficient of the independent variable by its mean value to get the absolute reduction in the mean of the dependent variable from driving the mean value of the independent variable to zero (as in Aggarwal et al. 2009). Then the relative reduction is obtained by dividing this absolute reduction by the mean of the dependent variable.

3.7.1 Fama-MacBeth Cross-sectional Regressions for CEF Premiums [Please place table 3.6 about here.]

The regression results for the monthly Fama-MacBeth cross-sectional regressions of CEF premium levels on various potential determinants for the period 2001-2010 are reported in table 3.6. We find that the average explanatory power of the regressions increases from a mean R2 of 12.69% [run (2)] when only is included to 27.88% [run (3)] when the systematic-risk exposures of the arbitrage portfolio are also included to 67% [run (6)] when all the potential determinants of CEF premiums considered herein are included. The mean coefficient estimate of the sensitivity of the net returns of the long CEF/short NAVPS

51 position on the market, HML and momentum factors are statistically insignificant implying that the average factor loadings of these risks do not significantly affect the changes in the CEF dollar premium. However, the significant (negative) coefficient for the SMB factor implies that the Fama-French size factor contributes to the cross-sectional variation in CEF dollar premiums. This finding of hedging difficulties with the SMB factor is consistent with a behavioral explanation of the CEF premium given that Qui and Welsh (2006) find that proxies for market sentiment are correlated with small stock returns but not with CEF premiums.

Since the mean coefficient estimate for is consistently negative and highly significant, CEF premiums become less positive or more negative as idiosyncratic volatilities increase. When we multiply the estimated coefficients of in table 3.6 by the ratio of the mean to the mean CEF premium from table 3.4, we estimate that a 1% change in

results in a CEF premium change ranging from 9.74% to 17.64%. We obtain the impact when by first multiplying the estimated coefficients of from table 3.6 by the mean from table 3.4 to get the absolute reductions in the mean CEF premium that range from 68.05% to 123.18%. Then we divide these absolute reductions by the mean CEF premium from table 3.4 to get the relative increases in the mean CEF premium that range from 12.1 to 21.9 times.

The mean coefficient estimates for are consistently negative as expected but their statistical significances change considerably between runs 4, 5 and 6. However, the importance of is marginal since a one percentage change in changes the premium by 0.002%. The mean coefficient estimate of is positive and highly significant only in run (5) where its importance is marginal since a one percent increase in this variable only increases the premium by 0.06%. The significance for

disappears when control variables for transaction costs and managerial characteristics are included in the regressions. The mean coefficient estimate of holding cash has its expected negative sign but becomes insignificant when all the independent variables are included in regression runs (5) and (6). The mean coefficient of has its expected negative sign even after adding all the other control variables. An increase of 1% in bond holdings leads to a 0.07% decrease in the CEF premium.

The mean coefficient estimate of is positive and highly significant. When the

(i.e., the difference in liquidities between the CEF and its asset holdings) is eliminated (i.e.,

52 change in would lead to an increase of 1.4% in the CEF premium. This is consistent with our expectation and the findings of Datar (2001) and Deli and Varma (2002). The highly significant mean coefficient estimate of of 0.51 implies that a one percent increase in the performance of the CEF manager would increase a positive or decrease a negative CEF premium by 0.31%. The mean coefficient estimate for gross Leverage is negative and significant as expected but becomes marginally significant when all potential determinants are considered [run (6)]. Thus, all the three potential benefits of the CEF in the conceptual model discussed earlier are statistically significant with their expected signs. Given the same level of risk of the arbitrage position, an increase in either liquidity or managerial contribution increases the CEF premium while an increase in gross leverage decreases the CEF premium.

The mean coefficient estimate of (i.e., natural log of market value as a proxy for arbitrage costs) is negative and highly significant as expected, which implies that the CEF premium decreases as firm size increases. Thus, a 1% increase in this variable would decrease the CEF premium by 0.06%. The mean coefficient estimate of ⁄ (i.e., inverse of the CEF’s price and another proxy for arbitrage costs) is positive and highly significant. Thus, a 1% increase in the inverse of the CEF’s price would lead to a 1.04% increase of the CEF premium. The mean coefficient estimate of (i.e., CEF dividend yield) is positive but not significant at conventional levels. While Pontiff (1996) did not find any statistical significance for the two size variables [ and ], he argues that the CEF premium would be higher due to the higher cost of an arbitrage trade to take advantage of the CEF premium for small and low priced CEFs.19

The mean coefficient estimate of is negative and strongly significant as expected. A 1% increase in would only marginally change the CEF premium by -0.2%. The mean coefficient estimate for is positive, and statistically and economically significant, since an increase in by 1% would increase the CEF premium by 9.91%.

3.7.2 Fama-MacBeth Cross-sectional Regressions for CEF premiums with Idiosyncratic Risk Conditioned on Past CEF Performance

[Please place table 3.7 about here.]

19 _{Pontiff (1996) reports that the median and mean R-squares increase from 11.77% to 22.73% and 14.75 to}

27.16%, respectively, with the addition of these three variables: dividend yield, natural log of market value and inverse of CEF price.

53 We now explore the relationship between the premium levels and idiosyncratic volatilities when the latter is conditioned on the sign of the change in the CEF price as reported in table 3.7. Similar to our results in tables 3.6, the average explanatory power exceeds 60% for the regression with all potential determinants. When only the arbitrage risk proxies are included and is conditioned using the previous month’s CEF price, the average explanatory power increases from 23.55% [table 3.6, run (1)] to 30.20% [table 3.7, run (2)]. Similar to our findings in table (3.6), the mean coefficient estimates for the systematic risk factors for the net return position are statistically insignificant except for . The mean estimate of is negative and statistically significant regardless of the sign of the previous month’s CEF price change, although the negatively conditioned loses its significance when all CEF premium determinants are included in run (4). The decrease in the premium ranges from 17.95% to 26.70% for a 1% decrease in a positively conditioned and from 3.50% to 4.69% for its negatively conditioned equivalent. When , we find that the premium is positive with maximum absolute value changes of 150% and 30.50% when conditioned on positive and negative previous month’s CEF prices, respectively.

The results for all the other variables reported in table (3.7) generally are consistent with our findings reported earlier in table (3.6). The mean coefficient estimate of gross

is still significantly negative. Unlike our results reported in table (3.6), the mean estimate of

is positive and significant at the 10% level and a 1% change in now only leads to a change of 0.01% in the CEF premium. The mean coefficient estimate of is positive and highly significant so that a 1% increase in would increase the CEF premium by 0.13%. Similar to table (3.6), coefficients estimates of and are negative and statistically significant, while those for , and are statistically insignificant at conventional levels.

[Please place table 3.8 about here.]

At this point, we summarize our findings from tables 3.6 and 3.7 with our expectations for each determinant in table 3.8. The principal arbitrage risk determinant represented by

is negative and statistically significant for all the regression runs. Only one of the hedge completeness proxies for systematic risk exposures (namely, ) is consistently

significantly different from zero. Consistent with the first hypothesis, the three CEF benefits are statistically significant with their expected signs. Specifically, we find that our proxies for relative liquidity ( ) and managerial contributions to value ( ) are associated with

54 an increase in the value of the CEF versus its NAVPS, and that for gross Liquidity is associated with a decrease in the value of the CEF versus its NAVPS. In our second hypothesis, we argued that if the arbitrageur knows exactly what the CEF holdings are, she can more accurately form the arbitrage position. We also argued that the type of the CEF holdings increase the cost of the arbitrage position either because of uncertainty and asymmetry of the NAVPS returns ( ) or because of their lower expected returns (e.g. cash and bonds) compared to the higher expected rate of return expected on an all-equity CEF. We could not confirm our hypothesis about the weight of options most likely because the mean idiosyncratic skewness is close to zero but do so for cash and bonds where the mean coefficient estimates are consistently significant and negative as expected.

3.7.3 Fama–MacBeth Cross-sectional Regressions for Changes in CEF Premiums [Please place table 3.9 about here.]

Regression results reported in Table 3.9 for month-by-month changes in CEF premiums provide insights into the determinants of the mechanism that may cause CEF prices to recalibrate to their fundamental values. The average explanatory powers (R2) increase from 10.73% when conditional is the sole independent variable [run (1)] to 68.56% with the inclusion of all potential determinants [run (4)]. The mean coefficient estimate of is consistently negative and highly significant (not significant) when conditioned on the lagged positive (negative) monthly changes in the previous month’s CEF price. For the full model [run (4) in table 3.9], the magnitude of the coefficient estimate is considerably higher than in the other runs but its sign and statistical significance remain. For this full model, a 1% decrease in would result in a 4.3% decrease in the average monthly change in CEF premiums. The average monthly change in CEF premiums decreases by 251% (2.5 times) in relative terms if idiosyncratic risk is eliminated ( ). We once again observe that only is significantly different from zero. The mean coefficients of

, , , and are insignificant at conventional levels.

The mean coefficient estimate for is positive and highly significant in run (3) but becomes insignificant in run (4) for the full model. The mean coefficient estimates of

, , and DY are all insignificant in run (4). The mean coefficient estimate of ⁄ is positive and significant at the 10% level in run (4), which indicates that a 1% increase in this variable would lead to a 0.05% decrease in the change of the CEF

55 premium. The mean coefficient estimate for is negative and statistically significant at conventional levels.